Due to the dramatic growth of total installation and individual capacity make the failures of wind turbines costly or even unacceptable. Therefore, wind turbine fault diagnosis, which is considered as a useful tool to ensuring the safety of wind turbines and reducing costly system maintenances, is attracting increasing attention. In this paper, a novel fault diagnosis for wind turbine gearbox based on basis pursuit denoising (BPDN) and the union of redundant dictionary is proposed. The union of redundant dictionary is constructed based on the underlying prior information of vibrations signal with multicomponent coupling effect. Within the frame work of BPDN, sparse coefficient and corresponding time-frequency atoms can be obtained. By time-frequency representation of the reconstructed signal, fault information can be displayed. Finally, an engineering application of a wind turbine gearbox is used to verify the effectiveness of the proposed method.